The manner in which the inventive apparatus or method proceeds is based on a linear scanning of the specimen, as opposed to known classical approaches which are based on rotations of either the sample or the illumination beam, which are based on the illumination with plane waves, which orientation is successively modified in order to acquire angular information. On the contrary, the inventive apparatus or method relies on a specially shaped illumination, which provides straightforwardly an angular distribution in the illumination of the specimen. The specimen can thus be linearly scanned in the object plane in order to acquire the data set enabling tomographic reconstruction, where the different positions directly possess the information on various angles for the incoming wave vectors. As the standard methods for tomographic reconstruction are typically assuming a plane illumination, the proposed approach requires a dedicated reconstruction method, which takes into account the wave profile employed for illumination, either by pre-processing the measured information to enable its use through standard methods, or by employing specific methods directly considering the particular engineered illumination employed. As for standard methods, the proposed approach based on a specially engineered illumination called structured wavefront and linear scanning can be employed through a so-called projection formalism, in which a real measurement of either the amplitude or the phase of the wave having interacted with the specimen can provide the three-dimensional distribution of respectively the absorption or the refractive index of the specimen. It is also possible to employ more general formalisms considering the diffraction theory, in which case a measurement of the full information of the wave (amplitude and phase) is required for tomographic reconstruction of the three-dimensional dielectric information of the specimen.
The theoretical foundations for tomography based on coherent imaging were proposed at the end of the sixties by Wolf and then Dändliker et al. (Wolf, 1969; Dändliker and Weiss, 1970). These seminal publications stated the relations between multiple frames acquired in various conditions—such as different illumination angles or different monochromatic wavelengths—and the information they provide on the three-dimensional volume, based on a diffraction formalism. In order to enable an analytical representation of the problem, one has usually to resort to an approximation of diffraction at first order, chosen either as the Born or as the Rytov approximations, as described for example in Born and Wolf, 1999.
The problem of resolving the integrated information along the optical axis in microscopy has been addressed in many various ways in the last decades, through typically different implementations enabling sectioning along the optical axis. One of the most widely known methods enabling sectioning is confocal microscopy, where the out-of-focus information is discarded before acquisition. While this type of methods enable 3D imaging in microscopy, they rely on principles of optical sectioning, which are not directly related to the approach of the proposed method. The sectioning typically requires the detection of a small 3D volume coupled with scanning procedures to recover the 3D information. Another widely known approach is the optical coherence tomography (OCT). As its name indicates, it is based on the exploitation of coherence properties of the light source with an interferometric detection scheme. OCT methods are based typically on reflection measurements, and rely on the spectral bandwidth of coherent light to generate an optical sectioning effect.
On the contrary of these known three-dimensional imaging methods, which are based on a sectioning property at detection, the proposed approach relies on the full-field detection of wave fields scattered by the specimen illuminated at various angles, which can be combined at post-processing stage in order to synthetically reconstruct the three-dimensional information. In this context, the first reconstruction methods proposed for practical applications were based on computer tomography (CT)—commonly called straight ray tomography—thus neglecting diffraction (Kak and Slaney, 1987). The use of this type of algorithm was justified by their extensive use for CT applications. Similar methods taking into account light diffraction were also proposed (Devaney, 1982).
In the context of microscopy, two main approaches were explored for acquisition of data based on angular scanning, consisting either in rotating the object, or to scan the beam around the object. These two methods were explored in various studies (Noda et al., 1992; Lauer, 1998; Lauer, 1999), and lead to different reconstruction resolutions. The two methods however rely always on the fundamental approach proposed in the sixties, and thus always require planar waves for illumination. Recently, various applications could be demonstrated with these methods, leading to high resolution with both the object rotation (Charrière et al., OL, 2006; Charrière et al., OX, 2006) and with the beam scanning (Choi, 2007; Debailleul, 2008; Sung, 2009).